We study local and global well posedness of the k-generalized Korteweg-de Vries equation in weighted Sobolev spaces Hs(R) ∩ L2(|x|2rdx).

Abstract In this paper, we show that Orlicz–Sobolev spaces $$W^{1,\varphi }(\varOmega )$$ W 1 , φ ( Ω ) can be characterized with the ACL- and ACC-characterizatio...

We survey recent results on the approximation of functions from Sobolev spaces by stochastic linear algorithms based on function values. The error is measured in various Sobolev norms, including positive and negative degree of smoothness. We also prove some new, related results concerning integration over Lipschitz domains, integration with variable weights, and study tractability of generalize...

The object of this note is the announcement of some results involving integration on [ — <», <*> ] with respect to functions whose values are operators into an intermediate space (see Definition B). Besides several other function spaces of interest in analysis, Sobolev and Lebesgue spaces are particular types of intermediate spaces (cf., the recent contributions of CALDERÓN, GAGLIARDO, KREIN, L...

A criterion for the approximability of all solutions heat equation in a bounded cylindrical domain that belong to Lebesgue class by more regular (e.g., Sobolev) same with larger base is obtained. Namely, complement smaller one must have no (nonempty connected) compact components. As an important corollary, we prove theorem on existence doubly orthogonal basis corresponding pair Hilbert spaces.